Her fiance, fellow detective Jake Peralta, has a doozy of a last case for he and Amy to solve as detectives. He presents her with a serial arson case that seem to be connected to the Saturday crossword puzzle. Amy, as a crossword fiend, is overjoyed.

Two different buildings have been set ablaze on two consecutive Saturdays, each with a puzzle left at the crime scene. The only other clue is a note sent to the puzzle’s “author” — not constructor, oddly — Melvin Stermley.

Amy immediately geeks out, mentioning that Stermley once created a puzzle where every word in the grid was the word “puzzle” in a different language. Jake then mentions that Stermley himself is coming in to help them with the case.

While Jake expects Melvin Stermley to be “a massive dork,” he turns out to be a handsome Hollywood tough guy type. Jake is instantly jealous. (For a nice bit of insider fun, Stermley is played by David Fumero, the husband of Melissa Fumero, who plays Amy Santiago.)

Amy has set up a display with both of Stermley’s puzzles connected to the fires, and the trio begin searching for leads. When Jake asks if he has the typical physique of a puzzler, he mentions that each puzzle only pays a couple hundred bucks, so he makes most of his money modeling. (No doubt a common response you’d get from any top constructor, right, folks?)

They read over the arsonist’s letter again: “Your clues I discombulate, to teach you to conjugate. The fool who fails to validate will watch as I conflagrate.”

Stermley suggests that they look at the answer grids of his puzzles for clues. Amy then jumps to anagramming some of the answer words. (The puzzler notes that Amy Santiago anagrams to “o, nasty amiga” and Jake Peralta to “eat a jerk, pal.”) Amy and Vin decide to split up the odd and even clues, leaving Jake out.

Getting nowhere with the anagrams, they wonder if “conjugate” in the arsonist’s letter means they should focus on the verbs, “the second best form of speech, after prepositions.” Jake suggests a different path, starting with possible suspects who don’t like Stermley, and the puzzler mentions the crossword night he’s hosting at a local bar. “It’s a total puz-hang,” according to Amy, and a good place to start looking.

While waiting in line outside the bar, Jake is disappointed no one is dressed like The Riddler. Amy points out someone wearing crossword-patterned pants. (Again, a common sight at the ACPT.) They chat with one of the other people in line, a woman who jokingly refers to Stermley as her future husband.

Before anyone can enter, they have to solve one of Stermley’s puzzles. Amy is tasked with anagramming the phrase “MEET A BRAINIER STUD, A” into the name of a place in the world. (Jake’s jealousy is piqued by the anagrammed message, of course.)

She quickly solves it — UNITED ARAB EMIRATES — and heads inside. But when Jake tries to follow, he discovers he has to solve a puzzle of his own to get in. The phrase “SAD ANUS LOSER, I GO IN” must be anagrammed into a film based on a classic book. Cut to Jake sneaking into the bathroom, because he couldn’t solve the anagram.

(It was DANGEROUS LIAISONS, by the way.)

While Jake waits in the bathroom for his pants to dry — he stepped into the toilet while climbing down from the window — two puzzle fans come in, discussing Stermley’s mad puzzle skills and how “Sam” must be pissed, as Stermley replaced him doing the Saturday crossword, bumping him down to work in Parade Magazine.

They mention Sam’s toughest clue, “a 5-letter word for a game popular in nursing homes,” to which Jake replies “BINGO.”

Jake mentions it to Stermley, who says Sam Jepson is one of his best friends and has been out of town for weeks. Jake still thinks Jepson is a solid lead.

Amy and Stermley, meanwhile, have realized that both targeted buildings were at the intersection of numbered streets, and those numbered intersections also point to letters in Stermley’s puzzles: M and A. They plan to build a trap into Stermley’s next puzzle to catch the arsonist.

When given a choice between Jake’s approach and Stermley’s, Amy opts to go with the puzzle trap.

Back at the precinct, Amy has determined that the most common letters in people’s names that follow MA are L, X, R, and T — Malcolm, Max, Mark, and Matthew, for example — so Stermley constructs a puzzle using only one of each of those letters. (A pretty daunting challenge, but definitely doable — especially if the cryptic-style crossword grid on the board behind Amy is the puzzle in question. It would have fewer intersections.)

Amy plans to stake out the intersections for each of those four letters, assigning one of them to Jake. (Jake, meanwhile, makes a secret plan to have Charles stake out Sam Jepson’s apartment.)

Charles spots Sam on the move — played by crossword guru Will Shortz, no less! — and Jake leaves his assignment to intercept. He and Charles follow Sam, who sits at a corner and eats soup, then calls his Mom. It turns out he has been out of town, only having returned tonight — and his marriage proposal was rejected. Bummer.

Jake returns to his assigned intersection, and the building is on fire. He has missed the arsonist.

Amy is understandably upset with Jake when they’re back at the office. Jake confesses he’s jealous of Stermley and doesn’t want Amy to wake up one day, regretting not marrying someone as smart as her. She reassures him that he’s a brilliant detective and that’s why she wants to marry him.